The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A047890 Number of permutations in S_n with longest increasing subsequence of length <= 5. 10
 1, 2, 6, 24, 120, 719, 5003, 39429, 344837, 3291590, 33835114, 370531683, 4285711539, 51990339068, 657723056000, 8636422912277, 117241501095189, 1639974912709122, 23570308719710838, 347217077020664880, 5231433025400049936, 80466744544235325387 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..250 F. Bergeron and F. Gascon, Counting Young tableaux of bounded height, J. Integer Sequences, Vol. 3 (2000), #00.1.7. Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, Jean-Marie Maillard, Stieltjes moment sequences for pattern-avoiding permutations, arXiv:2001.00393 [math.CO], 2020. Shalosh B. Ekhad, Nathaniel Shar, and Doron Zeilberger, The number of 1...d-avoiding permutations of length d+r for SYMBOLIC d but numeric r, arXiv:1504.02513, 2015. Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257-285. Nathaniel Shar, Experimental methods in permutation patterns and bijective proof, PhD Dissertation, Mathematics Department, Rutgers University, May 2016. FORMULA a(n) ~ 9 * 5^(2*n + 25/2) / (512 * n^12 * Pi^2). - Vaclav Kotesovec, Sep 10 2014 MAPLE h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul(mul(1+l[i]-j +add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n) end: g:= proc(n, i, l) `if`(n=0 or i=1, h([l[], 1\$n])^2, `if`(i<1, 0, add(g(n-i*j, i-1, [l[], i\$j]), j=0..n/i))) end: a:= n-> g(n, 5, []): seq(a(n), n=1..30); # Alois P. Heinz, Apr 10 2012 # second Maple program a:= proc(n) option remember; `if`(n<6, n!, ((-375+400*n+843*n^2 +322*n^3+35*n^4)*a(n-1) +225*(n-1)^2*(n-2)^2*a(n-3) -(259*n^2+622*n+45)*(n-1)^2*a(n-2))/ ((n+6)^2*(n+4)^2)) end: seq(a(n), n=1..30); # Alois P. Heinz, Sep 26 2012 MATHEMATICA h[l_] := With[{n = Length[l]}, Sum[i, {i, l}]!/Product[Product[1+l[[i]]-j+Sum[If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]]; g[n_, i_, l_] := If[n == 0 || i == 1, h[Join[l, Array[1&, n]]]^2, If[i<1, 0, Sum[g[n-i*j, i-1, Join[l, Array[i&, j]]], {j, 0, n/i}]]]; a[n_, k_] := If[k >= n, n!, g[n, k, {}]]; Table[a[n, 5], {n, 1, 30}] (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *) CROSSREFS A column of A047888. Cf. A005802, A052399. Column k=5 of A214015. Sequence in context: A224287 A248838 A052398 * A297204 A071088 A177533 Adjacent sequences: A047887 A047888 A047889 * A047891 A047892 A047893 KEYWORD nonn,easy AUTHOR Eric Rains (rains(AT)caltech.edu), N. J. A. Sloane EXTENSIONS More terms from Naohiro Nomoto, Mar 01 2002 More terms from Alois P. Heinz, Apr 10 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 26 16:14 EST 2023. Contains 359833 sequences. (Running on oeis4.)